930 CARNOT’S CYCLE IN THERMODYNAMICS.—MACGREGOR, 
the melting points at higher and lower pressures respectively. 
Now it may be proved by the aid of the First Law of Thermo- 
dynamics alone that the melting point of a substance which 
contracts on liquefying must lower as the pressure rises. It was 
so proved originally by Professor James Thomson.* Hence, in 
this case, t is a higher temperature than ¢. It follows that in 
this case heat is emitted during the operation AB when the 
temperature of the working substance is low, and absorbed 
during CD when its temperature is high. 
In the case of a working substance which is partly in the 
solid and partly in the liquid state and which expands on lique- 
faction, A Band D C will again be straight lines parallel to O v. 
In this case, however, since absorption of heat at constant 
pressure means increase of volume ¢’ is a higher isentropic than 
d. Also, it may be proved by the aid of the First Law of 
Thermodynamics alone by an argument similar to that of Prof. 
James Thomson, referred to above, that in this case the melting 
point rises as the pressure increases, and therefore that ¢ is a 
higher temperature than ¢. Hence, in this case, heat is absorbed 
during A B when the temperature is high and emitted during 
C D when the temperature is low. 
Hence, in the case of all kinds of working substances, Carnot’s 
Cycle when carried out so that work is done against external 
forces, involves absorption of heat when the substance is at a 
high temperature and emission of heat when at a low tempera- 
ture. 
And the differences in the above arguments by which this 
result is reached in the case of «lifferent kinds of substances seem 
to shew that it is not sufficient to prove it for one and tben 
assume it for all, but that it should be proved for all before 
being regarded as universally applicable. : 
* Trans. Roy. Soc., Edin., Jan. 2, 1849; Sir Wm. Thomson’s Mathematical and Physical 
Papers, Vol. I, p. 156. 
i” | 
